SHOWCASE TIME: Jimmer Fredette, who averaged 22.1 points last season for BYU, was scheduled to work out with the Knicks today.Getty Images

The Knicks are not going to turn their fortunes around in this June’s NBA draft, but at the very least, team president Donnie Walsh is bent on finding a diamond in the rough with one of his two second-round picks.

Walsh would love to find a rotation player to fill out their bare roster heading into the free-agent feast on July 1. (The Knicks’ lottery pick is the property of Utah.)

Today, the Knicks’ draft search heats up when they begin pre-draft workouts at their Westchester campus, bringing in sharp-shooting guard, Brigham Young’s Jimmer Fredette and Tennessee senior Bobby Maze, whom scouts do not believe will be drafted. But Walsh won’t be at the workouts today because he flew to Paris for the European final four.

The Knicks have the 38th and 39th picks. Fredette is expected to fall in that range. One league executive said he is a Mark Price-type of player, and coach Mike D’Antoni always is looking for strong perimeter players.

Fredette, from upstate Glens Falls, averaged 22.1 points as a junior and has until tomorrow’s deadline to pull out of the draft, because he hasn’t hired an agent.

Walsh said he prefers free agency were held before the draft — like in the NFL — so teams would have a clearer idea on their needs and whether they need all their cap space.

Walsh faces a dilemma on whether to package the picks and trade up into the first round. Walsh said he will explore that option only if the Knicks fall in love with a player. The guaranteed salary for a late first-round pick is more than $1 million, which could be precious cap space used up. Second-round picks do not have guaranteed pacts and are slotted at an estimated $450,000.

The Knicks could use one of their second-round picks on a European and keep him overseas. Two European centers could be in the mix, 6-foot-11 Miroslav Raduljica and Germany’s 7-foot Tibor Pleiss.

The Knicks likely would be thrilled if Cincinnati’s Lance Stephenson, of Lincoln High in Brooklyn, fell out of the first round. Stephenson was a surprise early entrant and has until tomorrow to pull out.

Other collegiates expected to go in the second round are Louisville’s Samando Samuels, West Virginia’s Da’Sean Butler, whose stock has dropped because of an Achilles injury, and Syracuse point guard Andy Rautins.

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Knicks point guard Sergio Rodriguez told Spanish-based Hoopshype.com he thinks the Knicks and Walsh are interested in re-signing him.

“They want me for next year, but they are waiting to see what they do with the rest of the [free agents],” Rodriguez said. “I spoke with Donnie in my exit interview. He was happy with what I had done.”

It still seems unlikely, because in April, D’Antoni stopped referring to Rodriguez as part of the team’s future.

It’s clear the Knicks won’t tender Rodriguez his $2.7 million qualifying offer, making him an unrestricted free agent.

But if the Knicks are desperate for a point guard, have leftover cap room, and he’s cheap, it’s not impossible Rodriguez could return to New York. Nevertheless, Real Madrid likely will outbid the Knicks.